The equation which is dimensionally consistent in the following is:
(Where $S_{n} =$ distance traveled by a body in $n^{t h}$ second, $u$ $=$ initial velocity, $a$ $=$ acceleration, $T$ $=$ time period, $r$ $=$ radius of the orbit, $M$ $=$ Mass of the sun, $G$ $=$ universal gravitational constant, $C$ $=$ RMS velocity, $P$ $=$ pressure and $d$ $=$ density.)

S_{n} = u + a (n - \frac{1}{2})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

T = \sqrt{\frac{4 π^{2} r^{3}}{G M}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C = \sqrt{\frac{3 p}{d}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A, B, C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D A, B, C
$S_{u} = u + a (n - \frac{1}{2})$ is derived from $S_{u} = (\frac{u}{n} + \frac{1}{2} g n^{2}) - (\frac{u}{n - 1} + \frac{1}{2} \frac{g}{(n - 1)^{2}})$
$\Rightarrow S n = u + a (\frac{n - 1}{2})$

$P = \sqrt{\frac{4 π^{2} R^{3}}{g m}} = \sqrt{\frac{L^{3}}{(M^{- 1} T^{- 2} C^{3}) (M^{1})}} = T^{1}$

$C = \sqrt{\frac{3 p}{d}} = L T^{- 1} = \sqrt{\frac{M^{1} L^{- 1} T^{- 2}}{M^{1} L^{- 3}}} = L T^{- 1}$
Hence, option D is correct.

Suggest Corrections

Similar questions

Q. A body moving with uniform acceleration travels a distance

s_{n}

= (0.4n + 9.8) m in

n^{t h}

second. Initial velocity of the body is (in

m s^{- 1}

)

A planet moves around sun in nearly circular orbit period of revolution 't', radius of orbit r mass of sun m.

Time period if direcyly proportional to mass of sun, distance between planet and sun and universal gravitational constant.

Prove T² is directly proportional to r³

A force acting on a body produces a constant acceleration. The equation written is as follows:

$F = K m \times \frac{(V - U)}{t}$

F- Force; K-constant;

m- mass; V- final velocity

U- initial velocity; t- time taken

a- acceleration; P- momentum

The equation can also be written as___ .

A body is moving with an initial velocity of $u$ and having constant acceleration $a$ . The final velocity $v$ can be obtained by using which of the following equation of motion if a body covers a distance $s$ .

Q. Check the correctness of the relation

S_{n t h} = u + \frac{a}{2} (2 n - 1)

, where

u

is initial velocity,

a

is acceleration and

S_{n t h}

is the distance travelled by the body in

n t h

second.

Join BYJU'S Learning Program

The correct option is D A, B, CSu=u+a(n−12) is derived from Su=(un+12gn2)−(un−1+12g(n−1)2)⇒Sn=u+a(n−12)P=√4π2R3gm=√L3(M−1T−2C3)(M1)=T1C=√3pd=LT−1=√M1L−1T−2M1L−3=LT−1Hence, option D is correct.